Season pork pieces generously with salt and pepper. Heat oil in a large stockpot over high heat. Once hot, add pork in batches and sear until golden on all sides (about 3–4 minutes per batch). Remove and set aside.

In the same pot, add chopped onion and sauté until soft. Stir in minced garlic, cumin, and oregano, cooking for 30 seconds more until fragrant.

Return pork to the pot. Pour in chicken broth and bring to a simmer. Reduce heat, cover, and cook for 2–4 hours until pork is tender and shreds easily. If needed, add more liquid to keep pork partially submerged.

Preheat oven to high broil. Line a baking sheet with foil or spray with oil. Arrange poblano chiles, jalapeños, and tomatillos cut-side down. Broil for 7–10 minutes until slightly charred and caramelized.

Transfer roasted peppers and tomatillos to a sealed plastic bag to steam for 5 minutes. Peel off the skins and discard.

In a blender, combine roasted vegetables and cilantro. Purée until smooth.

Add the green chile-tomatillo purée to the pork along with its braising juices. Stir to integrate and simmer for another 30–45 minutes until sauce thickens and melds with the pork.